The contribution of CO2 to climate change

Renowned climatologist Roger Pielke, Sr. has used IPCC's estimates of climate forcing to calculate the contribution of CO2 to recent climate change. Pielke makes very conservative (worst-case) assumptions in considering the impacts of greenhouse gases, black carbon, tropospheric ozone, and solar radiation. This analysis ignores land use changes, which have been demonstrated to affect climate in a significant way, and cosmic rays, which affect cloud cover and thus can lead to significant climate changes.

Pielke's estimate is that CO2 is responsible for 28% (at most) of the human-caused changes. If natural variations do occur (and it's very hard to argue that they do not) then this value decreases. But even if one assumes that the entire 0.6 deg C increase since 1900 is due to human effects, Pielke's estimate would suggest a CO2 contribution of only 0.17 deg C.
Modern temperatures remain lower than other periods within the Holocene (since the last Ice Age). Geologists and paleoclimatologists believe that the warmest conditions in the Holocene occurred several thousand years before Christ, and that several such episodes occurred. The most recent warm period occurred in medieval times 800-1200 years ago.
Richard A. Muller and Gordon J. MacDonald, “Chapter 1: Brief Introduction to the History of Climate” Ice Ages and Astronomical Causes 2000)

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